Combinatorial Prediction Markets

Robin HansonAssociate Professor of Economics, GMU

What do “we” believe?P = .25

P = .25

??Professions

AcademiaBet Odds

MediaPolls

Buy Low, Sell High

pricebuy

buy

sell

sell

Will price rise or fall?

E[ price change | ?? ]

Lots of ?? get tried,price includes all!

“Pays $1 if Obama wins”

(All are “gambling” “prediction” “info”)

Today’s Current Event Prices 65% Obama next US president15-22% Bird Flu confirmed in US by 2009 6-10% 9.0 Richter Earthquake by 200940-60% Yahoo CEO Yang resigns by 2009 3-15% US war act on N. Korea by 4/200920-21% Bin Laden caught by 4/200940-46% US or Israel air strike on Iran by 4/200928-30% US max tax rate > 40% in 201021-40% Any nation drop Euro by 2011 20-28% China war act on Taiwan by 201119-29% Google Lunar Prize won by 2013

Beats AlternativesVs. Public Opinion

I.E.M. beat presidential election polls 451/596 (Berg et al ‘01)

Re NFL, beat ave., rank 7 vs. 39 of 1947 (Pennock et al ’04)

Vs. Public ExpertsRacetrack odds beat weighed track experts (Figlewski ‘79)

• If anything, track odds weigh experts too much! OJ futures improve weather forecast (Roll ‘84) Stocks beat Challenger panel (Maloney & Mulherin ‘03)

Gas demand markets beat experts (Spencer ‘04)

Econ stat markets beat experts 2/3 (Wolfers & Zitzewitz ‘04)

Vs. Private ExpertsHP market beat official forecast 6/8 (Plott ‘00)

Eli Lily markets beat official 6/9 (Servan-Schreiber ’05)

Microsoft project markets beat managers (Proebsting ’05)XPree beat corp error, 3.5 vs 6.6%

“Prediction Market Accuracy in the Long Run”Joyce Berg, Forrest Nelson and Thomas Rietz, Jan. 2008.

Item 1988 1992 1996 2000 2004 All

# big polls

59 151 157 229 368 964

Poll “wins”

25 43 21 56 110 255

Market “wins”

34 108 136 173 258 709

% Market

58% 72% 87% 76% 70% 74%

P-value

0.148 0.000

0.000

0.000

0.000

0.000

Every nation*quarter:-Political stability-Military activity-Economic growth-US $ aid-US military activity& global, special& all combinations

Policy Analysis Market

Analysts often use prices from various markets as indicators of potential events. The use of petroleum futures contract prices by analysts of the Middle East is a classic example. The Policy Analysis Market (PAM) refines this approach by trading futures contracts that deal with underlying fundamentals of relevance to the Middle East. Initially, PAM will focus on the economic, civil, and military futures of Egypt, Jordan, Iran, Iraq, Israel, Saudi Arabia, Syria, and Turkey and the impact of U.S. involvement with each.

[Click here for a summary of PAM futures contracts]

The contracts traded on PAM will be based on objective data and observable events. These contracts will be valuable because traders who are registered with PAM will use their money to acquire contracts. A PAM trader who believes that the price of a specific futures contract under-predicts the future status of the issue on which it is based can attempt to profit from his belief by buying the contract. The converse holds for a trader who believes the price is an over-prediction – she can be a seller of the contract. This price discovery process, with the prospect of profit and at pain of loss, is at the core of a market’s predictive power.

The issues represented by PAM contracts may be interrelated; for example, the economic health of a country may affect civil stability in the country and the disposition of one country’s military may affect the disposition of another country’s military. The trading process at the heart of PAM allows traders to structure combinations of futures contracts. Such combinations represent predictions about interrelated issues that the trader has knowledge of and thus may be able to make money on through PAM. Trading these trader-structured derivatives results in a substantial refinement in predictive power.

[Click here for an example of PAM futures and derivatives contracts]

The PAM trading interface presents A Market in the Future of the Middle East. Trading on PAM is placed in the context of the region using a trading language designed for the fields of policy, security, and risk analysis. PAM will be active and accessible 24/7 and should prove as engaging as it is informative.

The Fuss:

Became:

Cummulative number of companies that have implemented an internal prediction market

(lower bound estimate)

0

5

10

15

20

25

30

35

1997 1998 1999 2000 2001 2002 2003 2004 2005 2006

Source:

Internal ApplicationsSales - HP, Google, Nokia, XPree, O’Reilly, Best BuyDeadlines - Siemens, Microsoft, MisysPick Project - Qualcomm, GE, Lily, Pfizer, Intercontinental HotelsUnknown - Novartis, GSK, Motorola, ArcelorMittal, Corning, Dentsu, Masterfoods, Thomson, Yahoo, Abbott, Chrysler, Edmunds, InfoWorld, FritoLay, Erickson, IHG, NBC, HVG, RAND, SAIC, SCA, TNT, Cisco, General Mills, Swisscom

Inputs Outputs

TheoryPrediction Markets

Status QuoInstitution

Compare! For Same

Not Experts vs. Self-chosen Amateurs

Forecasting Institution Goal:Given same participants, resources, topicWant most accurate institution forecasts

Separate question: who let participate?Can limit who can trade in market

Markets have low penalty for add foolsHope: get more info from amateurs?

Advantages

Numerically preciseConsistent across many issuesFrequently updatedHard to manipulateNeed not say who how expert whenAt least as accurate as alternatives

Ad Agency Decision Markets

$ Revenue if not Switch

E(R | not S)Compare!

$1 if not Switch

$ Revenue if Switch

E(R | S)

$1

P(S)

$1 if Switch

$ RevenueE(R)

Corporate Applications

E[ Revenue | Switch ad agency? ]E[ Revenue | Raise price 10%? ] E[ Project done date | Drop feature? ]E[ Project done date | Add personnel? ]E[ Stock price | Fire CEO? ]E[ Stock price | Acquire firm X? ]

Decision Market RequirementsLegal permission Outcome

MeasuredAggregate-enoughLinear-enoughConditional-enough

DecisionDistinct options Important enoughEnough influence

Public credibilityTraders

Enough informedDecision-insidersEnough incentivesAnonymity

PricesIntermediate-enoughCan show enough

US President Decision Markets

Politimetrics.com

Remake CEO Oversight For $1M!!

E[stock|fire CEO?] for all Fortune 500Subsidize cash trading, where legalExpect tons business press, CEOs look at

Manipulating CEOs add liquidity

Track firms follow advice, vs. notStatistically signif. diff. in few years

Sue boards that ignore advice w/o reason Shy boards then defer to market advice!!

Combo Betting

Yoopick Facebook Application

WinPlace

Show

All outcomes

Win Place Show

Not Not Not

Sport Finals TicketsUEFA EURO 2008

Austria

Croatia

Czech

Germany

Poland

Portugal

Switzerl.

Turkey

France

Greece

Italy

Netherl.

Romania

Russia

Spain ActualGame

Sweden

Ticket if Greece in FinalsGreece v.Croatia

PAM Scenario

Saudi Arabian

100

75

125

103

203

303

403

104

204

65

35

70

30

30

35

25

10

15

40

35

10

10094

Economic Health

New Price <IQcs403 85

Return to Focus ?TradeSAum3 03105-125

No Trade

Exit Issue

Max Up

Max Dn

10% Dn

10% Up

You Pick

62.47%

Bu

y S

ell

>IQcs403 85

Payoffs:

68.72%

56.79%

48.54%

95.13%

22.98%

+$2.74

-$15.34

+$34.74

$0.00 $0.00

-$2.61

-2.04

-$3.28

-$85.18

-$120.74

+$2.74

65

+$26.02

+1.43

+$96.61

& If

65%

Ave. pay<85 Select

$0.00

+0.34

-$1.07

-$19.72

-$1.12

-$6.31

-$22.22

%

Update

Execute a Trade ?Return to Form

ExecuteAbort trade if price has changed?

If US military involvement in Saudi Arabia in 3rd Quarter 2003 is not between 105 and 125, this trade is null and void. Otherwise, if Iraq civil stability in 4th Quarter 2003 is below 85, then I will receive $1.43, but if it is not below 85, I will pay $2.04.

Some Consensus Mechanisms

Competitive Forecasting – like surveyFormulas define consensus & score

Continuous Double Auctionmake or take offers to buy or sell

Call Auction – match accumulated offersMarket maker – always small spread

Old Tech Meets NewTo gain info, elicit probs p = {pi}i , Ep[x |A](Verify state i later, N/Q = people/questions)

Old tech (~1950+): Proper Scoring RulesN/Q 1: works well, N/Q 1: hard to combine

New tech (~1990+): Info/Predict MarketsN/Q 1: works well, N/Q 1: thin markets

The best of both: Market Scoring Rulesmodular, lab tests, compute issues, …

Opinion Pool “Impossibile”

Task: pool T(A) from opinions p1(A), p2(A), … Any 2 of IPP, MP, EB dictator (T= pd

) ! IPP = if A,B indep. in all pn, are indep. in TEB = commutes: pool, update on infoMP = commutes: pool, coarsen states field)

(MP T = n=0 wn pn , with wn indep. of A)

Really want pool via belief origin theoryGeneral solution: let traders figure it out?

Acc

urac

y

.001 .01 .1 1 10 100

Estimates per trader

Market Scoring Rules

Best of BothSimple Info Markets

thin marketproblem

Scoring Rulesopinion

poolproblem

Quantal Response ModularityNoisy choice: prob(act) exp(λ*payoff)When apply to a log MSR, get user reports (= new prices) independent of the last price:

isqii rP )|( qr

Simplifies inferences about beliefs from actsIgnores that harder to make complex changes

rationality liquidity

belief

reportstate

Laboratory Tests

Joint work with John Ledyard (Caltech), Takashi Ishida (Net Exchange)Trained in 3var session, return for 8varMetric: Kulback-Leibler i qi log(pi /qi) distance from market prices to Bayesian beliefs given all group info

Environments: Goals, TrainingWant in Environment:

Many variables, few directly related Few people, each not see all variables Can compute rational group estimatesExplainable, fast, neutral

Training Environment: 3 binary variables X,Y,Z, 23 = 8 combosP(X=0) = .3, P(X=Y) = .2, P(Z=1)= .5 3 people, see 10 cases of: AB, BC, AC Random map XYZ to ABC

Case A B C

1 1 -

1 2 1 -

0

3 1 -

0 4 1 -

0

5 1 -

0 6 1 -

1

7 1 -

1 8 1 -

0

9 1 -

0 10 0 -

0

Sum: 9 -

3

Same A B C

A -- --

4 B -- --

-- C -- --

--

(Actually: X Z Y )

Experiment Environment8 binary vars: STUVWXYZ28 = 256 combinations20% = P(S=0) = P(S=T) = P(T=U) = P(U=V) = … = P(X=Y) = P(Y=Z)6 people, each see 10 cases: ABCD, EFGH, ABEF, CDGH, ACEG, BDFHrandom map STUVWXYZ to ABCDEFGH

Case A B C D E F G H 1 0 1 0 1 - - - - 2 1 0 0 1 - - - - 3 0 0 1 1 - - - - 4 1 0 1 1 - - - - 5 0 1 1 1 - - - - 6 1 0 0 1 - - - - 7 0 1 1 1 - - - - 8 1 0 0 1 - - - - 9 1 0 0 1 - - - - 10 1 0 0 1 - - - -

Sum 6 3 4 10 - - - -

Same A B C D E F G H A -- 1 2 6 -- -- -- -- B -- -- 7 3 -- -- -- -- C -- -- -- 4 -- -- -- -- D -- -- -- -- -- -- -- -- …

(Really: W V X S U Z Y T )

-1

-0.5

0

0.5

1

0 5 10 15

MSR Info vs. Time – 3 Variables

0 5 10 15

Minutes

0

-1

1

% Info Agg. =

KL(prices,group)KL(uniform,group)

1-

MSR Info vs. Time – 255 prices

-1

-0.5

0

0.5

1

0 5 10 15

0 5 10 15

Minutes

0

-1

1

% Info Agg. =

KL(prices,group)KL(uniform,group)

1-

Combinatorial Lab Experiments

7 indep. prices from 3 folks in 4 min. Simple Double Auction < Scoring Rule ~ Opinion Pool ~ Combinatorial Call < Market Scoring Rule

255 indep. prices from 6 folks in 4 min.

Combinatorial Call ~ Simple Double Auction ~ Scoring Rule < Opinion Pool ~ Market Scoring Rule

Combo Market Maker Best of 5 Mechs

3 Variables = 8 States

0.000

0.050

0.100

0.150

0.200

0.250

0.300

KL

Dis

tanc

e

8 Variables = 256 States

0.600

0.800

1.000

1.200

1.400

1.600

KL

Dis

tanc

e

3 subjects, 7 prices, 5 minutes 6 subjects, 256 prices, 5 minutes

Compute TasksRepresent p(s), $(s,i)Add/settle var, Add/take $Browse E[x|A] & E[$|A]

& history of changes

For each E[x|A], show max/min/indifferent $ edits Allow edit of many E[x|A]

Update $(s,i) = b* log(p(s)) Avoid money pump errors

Edit structure?

How Close Markov Nets?Have no forseen error p alg.

But can distribute computation?Ways to browse E[x|A]Can allow edit if vars in same clique

How support other edits?Need good $(s) repr. to support:

For i take $, max edit, must find mins $(s,i)Update $ alg without forseen min $ error

How efficiently store histories?How allow structure changes?

Typical Problems In Field Now

Laws on gambling, insider trading“Moral” & “Culture” concernsNot really want to knowHard to find precise related eventsLittle participation for cheapNot enough events to validate, learnAwkward interfaces

ConcernsSelf-defeating prophecies Decision selection biasPrice manipulationInform enemiesShare less infoCombinatoricsMoral hazardAlarm publicEmbezzle

BozosLiesRich more “votes”Risk distortionBubbles

Simple Manipulation Model

0]or [

])[(

2

2])[(

0 ,0 ),(~ ),(~

),(~ ),(~ ),(~

)(],|)([max

])([max ]|[

22

2

22

2222

22

222

2

, 2

uwv

vv

uwv

x

z

PvEPvE

ccNN

uNuwNwvNv

cwvPvxE

wPPvzEzxuvEP

ManipulatorMarket maker

Informed trader

Equilibrium

Noise trader

Kyle Style Market Microstructure Game Theory

Lab DataAverage End of Period Prices

0

20

40

60

80

100

1 2 3 4 5 6 7 8

Period

Pri

ce

Non Manipulation

Manipulation

True Value

• 12 subjects, value = 0,40,100 • Each clue like “Not 100”. • 6 manipulators, get bonus for higher price• Manipulators bid higher• Others accept lower• Prices no less accurate

Hanson, Oprea, Porter JEBO, 2005

• 8 traders, Value = 0,100• Each Prob(Clue=V) = 2/3• 4 manipulators, bonus for price to hidden target 0,100

• 5 judges see prices, predict• Manipulators bid toward target• Prices and judges predictions no less accurate

R. Oprea, D. Porter, C. Hibbert, R. Hanson, D.Tila 2006

A Scaleable Implementation

Overlapping variable patchesA simple MSR per patchIf consistent, is Markov network

Var independent of rest given neighbors

Allow trade if all vars in same patchArbitrage overlapping patches

Sure to eventually agree, robust to gaming

Arbitraging Patches

.02 .08

.2 .7

A

B

B

A

.1

.9

.3 .1

.3 .3

C

.4

.6

C

B

B

.2

.734

1.000

.065Cash extracted

Arbitraging Patches Continued

.043 .171

.175 .611

A

B

B

A

.214

.786

.160 .053

.393 .393

C

.214

.786

C

B

B

.214

.786

But Arbitrage Is Not Modular

1. Everyone agrees on prices2. Expert on gets new info,

trades3. Arbitrage updates all prices 4. Expert on has no new info, but

must trade to restore old info!

LawDemocracy

Vote On Values Bet On BeliefsButE[ National Welfare | Alternative ] >?E[ National Welfare | Status Quo ]